Block #61,542

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 1:53:25 PM · Difficulty 8.9735 · 6,728,398 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

b1822e045272f18e20b0f2f1f02d15749e0547d47080d24b1464b9e4e7d9ff81

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Height

#61,542

Difficulty

8.973496

Transactions

Size

201 B

Version

Bits

08f93704

Nonce

145

Timestamp

7/18/2013, 1:53:25 PM

Confirmations

6,728,398

Merkle Root

d00c2f4fad9a317dbc242a49e2ff092b37f042898630f7d3d19b955ebcef3573

Transactions (1)

Coinbased00c2f4fad9a31…9b955ebcef3573

1 in → 1 out12.4000 XPM110 B

AK1JUKWL…oPR4rN5o

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.878 × 10⁹⁶(97-digit number)

38781224511454815341…24832127735298554491

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

3.878 × 10⁹⁶(97-digit number)

38781224511454815341…24832127735298554491

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.756 × 10⁹⁶(97-digit number)

77562449022909630683…49664255470597108981

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.551 × 10⁹⁷(98-digit number)

15512489804581926136…99328510941194217961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.102 × 10⁹⁷(98-digit number)

31024979609163852273…98657021882388435921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.204 × 10⁹⁷(98-digit number)

62049959218327704546…97314043764776871841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.240 × 10⁹⁸(99-digit number)

12409991843665540909…94628087529553743681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.481 × 10⁹⁸(99-digit number)

24819983687331081818…89256175059107487361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.963 × 10⁹⁸(99-digit number)

49639967374662163637…78512350118214974721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.927 × 10⁹⁸(99-digit number)

99279934749324327274…57024700236429949441

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer